The subterranean nation of Glot has developed the ability to “thermally link” two equally sized diamonds, such that they are always the same temperature, regardless of spatial separation. We can consider this “thermal linking” process “magic” (or sci-fi "thermal quantum entanglement"), but physics otherwise operate the same as in our universe. Contrary to this particular advancement, Glot has NOT discovered electricity. Otherwise, it has technology equivalent to the early-mid 1800's.
One of the diamonds is carefully immersed in one of their many magma–rivers, the other is put into a steam engine boiler. (These magma-rivers are part of a very large underground area, and are accessible, with precautions, at minimal cost.) Always at equal temperatures, the two diamonds boil/heat the steam, and “cool” the magma river respectively.
The “linking” process is far less expensive than the diamonds themselves, so they are cut into slices, half a millimeter in thickness to increase surface area. These slices are the smallest they can mount, without having them “wash” away in the magma river, while keeping the diamond in contact with the magma.
Without considering the cost of the diamonds: would this process actually work to produce a useful, geothermal powered, steam engine? (That doesn’t require shoveling, or even carrying fuel?)
If so, what mass of diamonds, in total, would be required to power an average steam locomotive of the 19th century?